The goal of this research is to develop new statistical methods for analyzing, interpreting, and designing clinical trials for patients with Acquired Immune Deficiency Syndrome (AIDS). Methods will be developed to model the relationship of repeated biological markers such as CD4 counts to clinical outcomes such as death. The primary purpose of this research is to study whether biological markers could be identified that may be used as early surrogates of clinical outcome. This would be useful for defining biological endpoints that may be used to determine treatmnt efficacy earlier than waiting for the clinical outcome to occur. A class of flexible group sequential designs will be developed which include lower boundaries for stopping a trial in favor of the null hypothesis as well as upper boundaries for stopping when there is a large treatment difference. The upper and lower boundaries will be defined by two "spending functions" which will dictate how much of a type I, as well as type II error, could be used as a function of time. These rethods could yield substantial savings in the average length of "AIDS" clinical trials compared to the methods currently used. Semiparametric estimates of parameters for the ordinary multiple linear regression model will be studied when the dependent variable is interval censored. The estimates proposed will be a generalization of the Buckley-James estimate for right censored data.